%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP185-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:25:37 PM UTC 2026
% Result : Unsatisfiable 8.01s 2.00s
% Output : CNFRefutation 8.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 19
% Syntax : Number of clauses : 204 ( 204 unt; 0 nHn; 115 RR)
% Number of literals : 204 ( 203 equ; 15 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 135 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t6,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t71,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t15,axiom,
sFlat0 = multiply(a,b),
introduced(definition) ).
cnf(t51,plain,
multiply(a,b) = sFlat0,
inference(orient,[status(thm)],[t15]) ).
cnf(t16,axiom,
sFlat1 = least_upper_bound(multiply(a,b),identity),
introduced(definition) ).
cnf(t3519,plain,
sFlat1 = least_upper_bound(identity,multiply(a,b)),
inference(step,[status(thm)],[t16,t71]) ).
cnf(t3520,plain,
sFlat1 = least_upper_bound(identity,sFlat0),
inference(step,[status(thm)],[t3519,t51]) ).
cnf(t3521,plain,
sFlat1 = least_upper_bound(sFlat0,identity),
inference(step,[status(thm)],[t3520,t71]) ).
cnf(t86,plain,
least_upper_bound(sFlat0,identity) = sFlat1,
inference(orient,[status(thm)],[t3521]) ).
cnf(t17,axiom,
sFlat2 = least_upper_bound(a,identity),
introduced(definition) ).
cnf(t3522,plain,
sFlat2 = least_upper_bound(identity,a),
inference(step,[status(thm)],[t17,t71]) ).
cnf(t89,plain,
least_upper_bound(identity,a) = sFlat2,
inference(orient,[status(thm)],[t3522]) ).
cnf(t18,axiom,
sFlat3 = least_upper_bound(b,identity),
introduced(definition) ).
cnf(t3523,plain,
sFlat3 = least_upper_bound(identity,b),
inference(step,[status(thm)],[t18,t71]) ).
cnf(t92,plain,
least_upper_bound(identity,b) = sFlat3,
inference(orient,[status(thm)],[t3523]) ).
cnf(t19,axiom,
sFlat4 = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
introduced(definition) ).
cnf(t36,plain,
multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = sFlat4,
inference(orient,[status(thm)],[t19]) ).
cnf(t75,plain,
multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) = sFlat4,
inference(rw,[status(thm)],[t36]) ).
cnf(t3707,plain,
multiply(least_upper_bound(identity,a),least_upper_bound(b,identity)) = sFlat4,
inference(step,[status(thm)],[t75,t71]) ).
cnf(t3708,plain,
multiply(sFlat2,least_upper_bound(b,identity)) = sFlat4,
inference(step,[status(thm)],[t3707,t89]) ).
cnf(t3709,plain,
multiply(sFlat2,least_upper_bound(identity,b)) = sFlat4,
inference(step,[status(thm)],[t3708,t71]) ).
cnf(t3710,plain,
multiply(sFlat2,sFlat3) = sFlat4,
inference(step,[status(thm)],[t3709,t92]) ).
cnf(t2500,plain,
multiply(sFlat2,sFlat3) = sFlat4,
inference(orient,[status(thm)],[t3710]) ).
cnf(t20,axiom,
sFlat5 = greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
introduced(definition) ).
cnf(t3524,plain,
sFlat5 = greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
inference(step,[status(thm)],[t20,t71]) ).
cnf(t3525,plain,
sFlat5 = greatest_lower_bound(least_upper_bound(identity,sFlat0),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
inference(step,[status(thm)],[t3524,t51]) ).
cnf(t3526,plain,
sFlat5 = greatest_lower_bound(least_upper_bound(sFlat0,identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
inference(step,[status(thm)],[t3525,t71]) ).
cnf(t3527,plain,
sFlat5 = greatest_lower_bound(sFlat1,multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
inference(step,[status(thm)],[t3526,t86]) ).
cnf(t3528,plain,
sFlat5 = greatest_lower_bound(sFlat1,multiply(least_upper_bound(identity,a),least_upper_bound(b,identity))),
inference(step,[status(thm)],[t3527,t71]) ).
cnf(t3529,plain,
sFlat5 = greatest_lower_bound(sFlat1,multiply(sFlat2,least_upper_bound(b,identity))),
inference(step,[status(thm)],[t3528,t89]) ).
cnf(t3530,plain,
sFlat5 = greatest_lower_bound(sFlat1,multiply(sFlat2,least_upper_bound(identity,b))),
inference(step,[status(thm)],[t3529,t71]) ).
cnf(t3531,plain,
sFlat5 = greatest_lower_bound(sFlat1,multiply(sFlat2,sFlat3)),
inference(step,[status(thm)],[t3530,t92]) ).
cnf(t109,plain,
greatest_lower_bound(sFlat1,multiply(sFlat2,sFlat3)) = sFlat5,
inference(orient,[status(thm)],[t3531]) ).
cnf(t3729,plain,
greatest_lower_bound(sFlat1,sFlat4) = sFlat5,
inference(step,[status(thm)],[t109,t2500]) ).
cnf(t2530,plain,
greatest_lower_bound(sFlat1,sFlat4) = sFlat5,
inference(rw,[status(thm)],[t3729]) ).
cnf(t2566,plain,
greatest_lower_bound(sFlat1,sFlat4) = sFlat5,
inference(orient,[status(thm)],[t2530]) ).
cnf(t5,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t25,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t9,axiom,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t76,plain,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t87,plain,
least_upper_bound(sFlat0,least_upper_bound(identity,X1)) = least_upper_bound(sFlat1,X1),
inference(cp,[status(thm)],[t76,t86]) ).
cnf(t181,plain,
least_upper_bound(sFlat0,least_upper_bound(identity,X1)) = least_upper_bound(sFlat1,X1),
inference(orient,[status(thm)],[t87]) ).
cnf(t1,axiom,
least_upper_bound(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t22,plain,
least_upper_bound(X1,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t80,plain,
least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2),
inference(cp,[status(thm)],[t76,t22]) ).
cnf(t175,plain,
least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2),
inference(orient,[status(thm)],[t80]) ).
cnf(t93,plain,
least_upper_bound(identity,least_upper_bound(b,X1)) = least_upper_bound(sFlat3,X1),
inference(cp,[status(thm)],[t76,t92]) ).
cnf(t283,plain,
least_upper_bound(identity,least_upper_bound(b,X1)) = least_upper_bound(sFlat3,X1),
inference(orient,[status(thm)],[t93]) ).
cnf(t290,plain,
least_upper_bound(identity,least_upper_bound(b,X1)) = least_upper_bound(identity,least_upper_bound(sFlat3,X1)),
inference(cp,[status(thm)],[t175,t283]) ).
cnf(t3564,plain,
least_upper_bound(sFlat3,X1) = least_upper_bound(identity,least_upper_bound(sFlat3,X1)),
inference(step,[status(thm)],[t290,t283]) ).
cnf(t597,plain,
least_upper_bound(identity,least_upper_bound(sFlat3,X1)) = least_upper_bound(sFlat3,X1),
inference(orient,[status(thm)],[t3564]) ).
cnf(t7,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t23,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t94,plain,
identity = greatest_lower_bound(identity,sFlat3),
inference(cp,[status(thm)],[t25,t92]) ).
cnf(t4,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t95,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t3533,plain,
identity = greatest_lower_bound(sFlat3,identity),
inference(step,[status(thm)],[t94,t95]) ).
cnf(t117,plain,
greatest_lower_bound(sFlat3,identity) = identity,
inference(orient,[status(thm)],[t3533]) ).
cnf(t118,plain,
sFlat3 = least_upper_bound(sFlat3,identity),
inference(cp,[status(thm)],[t23,t117]) ).
cnf(t124,plain,
least_upper_bound(sFlat3,identity) = sFlat3,
inference(orient,[status(thm)],[t118]) ).
cnf(t125,plain,
least_upper_bound(sFlat3,least_upper_bound(identity,X1)) = least_upper_bound(sFlat3,X1),
inference(cp,[status(thm)],[t76,t124]) ).
cnf(t377,plain,
least_upper_bound(sFlat3,least_upper_bound(identity,X1)) = least_upper_bound(sFlat3,X1),
inference(orient,[status(thm)],[t125]) ).
cnf(t90,plain,
least_upper_bound(identity,least_upper_bound(a,X1)) = least_upper_bound(sFlat2,X1),
inference(cp,[status(thm)],[t76,t89]) ).
cnf(t227,plain,
least_upper_bound(identity,least_upper_bound(a,X1)) = least_upper_bound(sFlat2,X1),
inference(orient,[status(thm)],[t90]) ).
cnf(t231,plain,
least_upper_bound(sFlat2,X1) = least_upper_bound(identity,least_upper_bound(X1,a)),
inference(cp,[status(thm)],[t227,t71]) ).
cnf(t514,plain,
least_upper_bound(identity,least_upper_bound(X1,a)) = least_upper_bound(sFlat2,X1),
inference(orient,[status(thm)],[t231]) ).
cnf(t13,axiom,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t27,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t58,plain,
multiply(a,least_upper_bound(b,X1)) = least_upper_bound(sFlat0,multiply(a,X1)),
inference(cp,[status(thm)],[t27,t51]) ).
cnf(t1184,plain,
least_upper_bound(sFlat0,multiply(a,X1)) = multiply(a,least_upper_bound(b,X1)),
inference(orient,[status(thm)],[t58]) ).
cnf(t10,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t26,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t3,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t61,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t3]) ).
cnf(t70,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t26,t61]) ).
cnf(t2,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t21,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t3606,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t70,t21]) ).
cnf(t989,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t3606]) ).
cnf(t991,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t989,t61]) ).
cnf(t1029,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t991]) ).
cnf(t996,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t989,t989]) ).
cnf(t1067,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t996]) ).
cnf(t3607,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t1029,t1067]) ).
cnf(t1077,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t3607]) ).
cnf(t1078,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t1077]) ).
cnf(t1188,plain,
multiply(a,least_upper_bound(b,identity)) = least_upper_bound(sFlat0,a),
inference(cp,[status(thm)],[t1184,t1078]) ).
cnf(t3616,plain,
multiply(a,least_upper_bound(identity,b)) = least_upper_bound(sFlat0,a),
inference(step,[status(thm)],[t1188,t71]) ).
cnf(t3617,plain,
multiply(a,sFlat3) = least_upper_bound(sFlat0,a),
inference(step,[status(thm)],[t3616,t92]) ).
cnf(t1208,plain,
least_upper_bound(sFlat0,a) = multiply(a,sFlat3),
inference(orient,[status(thm)],[t3617]) ).
cnf(t1211,plain,
least_upper_bound(sFlat2,sFlat0) = least_upper_bound(identity,multiply(a,sFlat3)),
inference(cp,[status(thm)],[t514,t1208]) ).
cnf(t3620,plain,
least_upper_bound(sFlat0,sFlat2) = least_upper_bound(identity,multiply(a,sFlat3)),
inference(step,[status(thm)],[t1211,t71]) ).
cnf(t1230,plain,
least_upper_bound(identity,multiply(a,sFlat3)) = least_upper_bound(sFlat0,sFlat2),
inference(orient,[status(thm)],[t3620]) ).
cnf(t1232,plain,
least_upper_bound(sFlat3,multiply(a,sFlat3)) = least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)),
inference(cp,[status(thm)],[t377,t1230]) ).
cnf(t14,axiom,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t30,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t14]) ).
cnf(t31,plain,
multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t30,t21]) ).
cnf(t236,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(identity,X2),X1),
inference(orient,[status(thm)],[t31]) ).
cnf(t3623,plain,
multiply(least_upper_bound(identity,a),sFlat3) = least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)),
inference(step,[status(thm)],[t1232,t236]) ).
cnf(t3624,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)),
inference(step,[status(thm)],[t3623,t89]) ).
cnf(t1240,plain,
least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)) = multiply(sFlat2,sFlat3),
inference(orient,[status(thm)],[t3624]) ).
cnf(t1242,plain,
least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)) = least_upper_bound(identity,multiply(sFlat2,sFlat3)),
inference(cp,[status(thm)],[t597,t1240]) ).
cnf(t3629,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(identity,multiply(sFlat2,sFlat3)),
inference(step,[status(thm)],[t1242,t1240]) ).
cnf(t1270,plain,
least_upper_bound(identity,multiply(sFlat2,sFlat3)) = multiply(sFlat2,sFlat3),
inference(orient,[status(thm)],[t3629]) ).
cnf(t1272,plain,
least_upper_bound(sFlat1,multiply(sFlat2,sFlat3)) = least_upper_bound(sFlat0,multiply(sFlat2,sFlat3)),
inference(cp,[status(thm)],[t181,t1270]) ).
cnf(t1751,plain,
least_upper_bound(sFlat1,multiply(sFlat2,sFlat3)) = least_upper_bound(sFlat0,multiply(sFlat2,sFlat3)),
inference(orient,[status(thm)],[t1272]) ).
cnf(t3717,plain,
least_upper_bound(sFlat1,sFlat4) = least_upper_bound(sFlat0,multiply(sFlat2,sFlat3)),
inference(step,[status(thm)],[t1751,t2500]) ).
cnf(t3718,plain,
least_upper_bound(sFlat1,sFlat4) = least_upper_bound(sFlat0,sFlat4),
inference(step,[status(thm)],[t3717,t2500]) ).
cnf(t2522,plain,
least_upper_bound(sFlat1,sFlat4) = least_upper_bound(sFlat0,sFlat4),
inference(rw,[status(thm)],[t3718]) ).
cnf(t2572,plain,
least_upper_bound(sFlat1,sFlat4) = least_upper_bound(sFlat0,sFlat4),
inference(orient,[status(thm)],[t2522]) ).
cnf(t2577,plain,
sFlat1 = greatest_lower_bound(sFlat1,least_upper_bound(sFlat0,sFlat4)),
inference(cp,[status(thm)],[t25,t2572]) ).
cnf(t2615,plain,
greatest_lower_bound(sFlat1,least_upper_bound(sFlat0,sFlat4)) = sFlat1,
inference(orient,[status(thm)],[t2577]) ).
cnf(t3721,plain,
least_upper_bound(identity,sFlat4) = multiply(sFlat2,sFlat3),
inference(step,[status(thm)],[t1270,t2500]) ).
cnf(t3722,plain,
least_upper_bound(identity,sFlat4) = sFlat4,
inference(step,[status(thm)],[t3721,t2500]) ).
cnf(t2524,plain,
least_upper_bound(identity,sFlat4) = sFlat4,
inference(rw,[status(thm)],[t3722]) ).
cnf(t3731,plain,
least_upper_bound(sFlat4,identity) = sFlat4,
inference(step,[status(thm)],[t2524,t71]) ).
cnf(t2536,plain,
least_upper_bound(sFlat4,identity) = sFlat4,
inference(orient,[status(thm)],[t3731]) ).
cnf(t2542,plain,
least_upper_bound(sFlat4,least_upper_bound(identity,X1)) = least_upper_bound(sFlat4,X1),
inference(cp,[status(thm)],[t76,t2536]) ).
cnf(t2749,plain,
least_upper_bound(sFlat4,least_upper_bound(identity,X1)) = least_upper_bound(sFlat4,X1),
inference(orient,[status(thm)],[t2542]) ).
cnf(t2758,plain,
least_upper_bound(sFlat4,least_upper_bound(b,X1)) = least_upper_bound(sFlat4,least_upper_bound(sFlat3,X1)),
inference(cp,[status(thm)],[t2749,t283]) ).
cnf(t98,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)),
inference(cp,[status(thm)],[t23,t95]) ).
cnf(t157,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t98]) ).
cnf(t74,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t25,t71]) ).
cnf(t126,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t74]) ).
cnf(t286,plain,
least_upper_bound(sFlat3,greatest_lower_bound(b,X1)) = least_upper_bound(identity,b),
inference(cp,[status(thm)],[t283,t23]) ).
cnf(t3545,plain,
least_upper_bound(sFlat3,greatest_lower_bound(b,X1)) = sFlat3,
inference(step,[status(thm)],[t286,t92]) ).
cnf(t293,plain,
least_upper_bound(sFlat3,greatest_lower_bound(b,X1)) = sFlat3,
inference(orient,[status(thm)],[t3545]) ).
cnf(t295,plain,
greatest_lower_bound(b,X1) = greatest_lower_bound(greatest_lower_bound(b,X1),sFlat3),
inference(cp,[status(thm)],[t126,t293]) ).
cnf(t8,axiom,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t99,plain,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t8]) ).
cnf(t3565,plain,
greatest_lower_bound(b,X1) = greatest_lower_bound(b,greatest_lower_bound(X1,sFlat3)),
inference(step,[status(thm)],[t295,t99]) ).
cnf(t612,plain,
greatest_lower_bound(b,greatest_lower_bound(X1,sFlat3)) = greatest_lower_bound(b,X1),
inference(orient,[status(thm)],[t3565]) ).
cnf(t615,plain,
greatest_lower_bound(b,X1) = greatest_lower_bound(b,greatest_lower_bound(sFlat3,X1)),
inference(cp,[status(thm)],[t612,t95]) ).
cnf(t825,plain,
greatest_lower_bound(b,greatest_lower_bound(sFlat3,X1)) = greatest_lower_bound(b,X1),
inference(orient,[status(thm)],[t615]) ).
cnf(t829,plain,
greatest_lower_bound(b,least_upper_bound(sFlat3,X1)) = greatest_lower_bound(b,sFlat3),
inference(cp,[status(thm)],[t825,t25]) ).
cnf(t3595,plain,
greatest_lower_bound(b,least_upper_bound(sFlat3,X1)) = greatest_lower_bound(sFlat3,b),
inference(step,[status(thm)],[t829,t95]) ).
cnf(t133,plain,
b = greatest_lower_bound(b,sFlat3),
inference(cp,[status(thm)],[t126,t92]) ).
cnf(t3536,plain,
b = greatest_lower_bound(sFlat3,b),
inference(step,[status(thm)],[t133,t95]) ).
cnf(t142,plain,
greatest_lower_bound(sFlat3,b) = b,
inference(orient,[status(thm)],[t3536]) ).
cnf(t3596,plain,
greatest_lower_bound(b,least_upper_bound(sFlat3,X1)) = b,
inference(step,[status(thm)],[t3595,t142]) ).
cnf(t928,plain,
greatest_lower_bound(b,least_upper_bound(sFlat3,X1)) = b,
inference(orient,[status(thm)],[t3596]) ).
cnf(t1241,plain,
b = greatest_lower_bound(b,multiply(sFlat2,sFlat3)),
inference(cp,[status(thm)],[t928,t1240]) ).
cnf(t1267,plain,
greatest_lower_bound(b,multiply(sFlat2,sFlat3)) = b,
inference(orient,[status(thm)],[t1241]) ).
cnf(t1268,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(multiply(sFlat2,sFlat3),b),
inference(cp,[status(thm)],[t157,t1267]) ).
cnf(t3632,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(b,multiply(sFlat2,sFlat3)),
inference(step,[status(thm)],[t1268,t71]) ).
cnf(t1317,plain,
least_upper_bound(b,multiply(sFlat2,sFlat3)) = multiply(sFlat2,sFlat3),
inference(orient,[status(thm)],[t3632]) ).
cnf(t3719,plain,
least_upper_bound(b,sFlat4) = multiply(sFlat2,sFlat3),
inference(step,[status(thm)],[t1317,t2500]) ).
cnf(t3720,plain,
least_upper_bound(b,sFlat4) = sFlat4,
inference(step,[status(thm)],[t3719,t2500]) ).
cnf(t2523,plain,
least_upper_bound(b,sFlat4) = sFlat4,
inference(rw,[status(thm)],[t3720]) ).
cnf(t3730,plain,
least_upper_bound(sFlat4,b) = sFlat4,
inference(step,[status(thm)],[t2523,t71]) ).
cnf(t2531,plain,
least_upper_bound(sFlat4,b) = sFlat4,
inference(orient,[status(thm)],[t3730]) ).
cnf(t2535,plain,
least_upper_bound(sFlat4,least_upper_bound(b,X1)) = least_upper_bound(sFlat4,X1),
inference(cp,[status(thm)],[t76,t2531]) ).
cnf(t2729,plain,
least_upper_bound(sFlat4,least_upper_bound(b,X1)) = least_upper_bound(sFlat4,X1),
inference(orient,[status(thm)],[t2535]) ).
cnf(t3768,plain,
least_upper_bound(sFlat4,X1) = least_upper_bound(sFlat4,least_upper_bound(sFlat3,X1)),
inference(step,[status(thm)],[t2758,t2729]) ).
cnf(t3172,plain,
least_upper_bound(sFlat4,least_upper_bound(sFlat3,X1)) = least_upper_bound(sFlat4,X1),
inference(orient,[status(thm)],[t3768]) ).
cnf(t3711,plain,
least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)) = sFlat4,
inference(step,[status(thm)],[t1240,t2500]) ).
cnf(t2501,plain,
least_upper_bound(sFlat3,least_upper_bound(sFlat0,sFlat2)) = sFlat4,
inference(orient,[status(thm)],[t3711]) ).
cnf(t3177,plain,
least_upper_bound(sFlat4,least_upper_bound(sFlat0,sFlat2)) = least_upper_bound(sFlat4,sFlat4),
inference(cp,[status(thm)],[t3172,t2501]) ).
cnf(t3769,plain,
least_upper_bound(sFlat4,least_upper_bound(sFlat0,sFlat2)) = sFlat4,
inference(step,[status(thm)],[t3177,t22]) ).
cnf(t3194,plain,
least_upper_bound(sFlat4,least_upper_bound(sFlat0,sFlat2)) = sFlat4,
inference(orient,[status(thm)],[t3769]) ).
cnf(t159,plain,
least_upper_bound(X1,X2) = least_upper_bound(least_upper_bound(X1,X2),X1),
inference(cp,[status(thm)],[t157,t25]) ).
cnf(t3553,plain,
least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,X1)),
inference(step,[status(thm)],[t159,t76]) ).
cnf(t445,plain,
least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X1,X2),
inference(orient,[status(thm)],[t3553]) ).
cnf(t1082,plain,
multiply(X1,least_upper_bound(identity,X2)) = least_upper_bound(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t27,t1078]) ).
cnf(t1636,plain,
least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(identity,X2)),
inference(orient,[status(thm)],[t1082]) ).
cnf(t2508,plain,
multiply(sFlat2,least_upper_bound(identity,sFlat3)) = least_upper_bound(sFlat2,sFlat4),
inference(cp,[status(thm)],[t1636,t2500]) ).
cnf(t3738,plain,
multiply(sFlat2,least_upper_bound(sFlat3,identity)) = least_upper_bound(sFlat2,sFlat4),
inference(step,[status(thm)],[t2508,t71]) ).
cnf(t3739,plain,
multiply(sFlat2,sFlat3) = least_upper_bound(sFlat2,sFlat4),
inference(step,[status(thm)],[t3738,t124]) ).
cnf(t3740,plain,
sFlat4 = least_upper_bound(sFlat2,sFlat4),
inference(step,[status(thm)],[t3739,t2500]) ).
cnf(t2638,plain,
least_upper_bound(sFlat2,sFlat4) = sFlat4,
inference(orient,[status(thm)],[t3740]) ).
cnf(t2643,plain,
least_upper_bound(sFlat2,least_upper_bound(sFlat4,X1)) = least_upper_bound(sFlat4,X1),
inference(cp,[status(thm)],[t76,t2638]) ).
cnf(t3010,plain,
least_upper_bound(sFlat2,least_upper_bound(sFlat4,X1)) = least_upper_bound(sFlat4,X1),
inference(orient,[status(thm)],[t2643]) ).
cnf(t3019,plain,
least_upper_bound(least_upper_bound(sFlat4,X1),sFlat2) = least_upper_bound(least_upper_bound(sFlat4,X1),least_upper_bound(sFlat4,X1)),
inference(cp,[status(thm)],[t445,t3010]) ).
cnf(t3798,plain,
least_upper_bound(sFlat4,least_upper_bound(X1,sFlat2)) = least_upper_bound(least_upper_bound(sFlat4,X1),least_upper_bound(sFlat4,X1)),
inference(step,[status(thm)],[t3019,t76]) ).
cnf(t3799,plain,
least_upper_bound(sFlat4,least_upper_bound(X1,sFlat2)) = least_upper_bound(sFlat4,least_upper_bound(X1,least_upper_bound(sFlat4,X1))),
inference(step,[status(thm)],[t3798,t76]) ).
cnf(t3800,plain,
least_upper_bound(sFlat4,least_upper_bound(X1,sFlat2)) = least_upper_bound(sFlat4,least_upper_bound(X1,sFlat4)),
inference(step,[status(thm)],[t3799,t445]) ).
cnf(t3801,plain,
least_upper_bound(sFlat4,least_upper_bound(X1,sFlat2)) = least_upper_bound(sFlat4,X1),
inference(step,[status(thm)],[t3800,t445]) ).
cnf(t3465,plain,
least_upper_bound(sFlat4,least_upper_bound(X1,sFlat2)) = least_upper_bound(sFlat4,X1),
inference(orient,[status(thm)],[t3801]) ).
cnf(t3802,plain,
least_upper_bound(sFlat4,sFlat0) = sFlat4,
inference(step,[status(thm)],[t3194,t3465]) ).
cnf(t3479,plain,
least_upper_bound(sFlat4,sFlat0) = sFlat4,
inference(rw,[status(thm)],[t3802]) ).
cnf(t3803,plain,
least_upper_bound(sFlat0,sFlat4) = sFlat4,
inference(step,[status(thm)],[t3479,t71]) ).
cnf(t3480,plain,
least_upper_bound(sFlat0,sFlat4) = sFlat4,
inference(orient,[status(thm)],[t3803]) ).
cnf(t3808,plain,
greatest_lower_bound(sFlat1,sFlat4) = sFlat1,
inference(step,[status(thm)],[t2615,t3480]) ).
cnf(t3809,plain,
sFlat5 = sFlat1,
inference(step,[status(thm)],[t3808,t2566]) ).
cnf(t3494,plain,
sFlat5 = sFlat1,
inference(rw,[status(thm)],[t3809]) ).
cnf(t3495,plain,
sFlat5 = sFlat1,
inference(orient,[status(thm)],[t3494]) ).
cnf(t3810,plain,
greatest_lower_bound(sFlat1,sFlat4) = sFlat1,
inference(step,[status(thm)],[t2566,t3495]) ).
cnf(t3496,plain,
greatest_lower_bound(sFlat1,sFlat4) = sFlat1,
inference(orient,[status(thm)],[t3810]) ).
cnf(goal_0,negated_conjecture,
greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[goal_0,t71]) ).
cnf(g0_1,plain,
greatest_lower_bound(least_upper_bound(identity,sFlat0),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_0,t51]) ).
cnf(g0_2,plain,
greatest_lower_bound(least_upper_bound(sFlat0,identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_1,t71]) ).
cnf(g0_3,plain,
greatest_lower_bound(sFlat1,multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_2,t86]) ).
cnf(g0_4,plain,
greatest_lower_bound(sFlat1,multiply(least_upper_bound(identity,a),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_3,t71]) ).
cnf(g0_5,plain,
greatest_lower_bound(sFlat1,multiply(sFlat2,least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_4,t89]) ).
cnf(g0_6,plain,
greatest_lower_bound(sFlat1,multiply(sFlat2,least_upper_bound(identity,b))) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_5,t71]) ).
cnf(g0_7,plain,
greatest_lower_bound(sFlat1,multiply(sFlat2,sFlat3)) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_6,t92]) ).
cnf(g0_8,plain,
greatest_lower_bound(sFlat1,sFlat4) != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_7,t2500]) ).
cnf(g0_9,plain,
sFlat1 != least_upper_bound(multiply(a,b),identity),
inference(rw,[status(thm)],[g0_8,t3496]) ).
cnf(g0_10,plain,
sFlat1 != least_upper_bound(identity,multiply(a,b)),
inference(rw,[status(thm)],[g0_9,t71]) ).
cnf(g0_11,plain,
sFlat1 != least_upper_bound(identity,sFlat0),
inference(rw,[status(thm)],[g0_10,t51]) ).
cnf(g0_12,plain,
sFlat1 != least_upper_bound(sFlat0,identity),
inference(rw,[status(thm)],[g0_11,t71]) ).
cnf(g0_13,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_12,t86]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP185-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 14:06:09 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.01/2.00 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.01/2.00 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------